Can't really say...during the rule of Charles X, the only major actions the French military undertook during his reign was the Battle of Navarino and the subsequent 15,000-strong expedition to the Morea during the later years of the Greek War of Independence (the latter continued into the deposition and installment of the July Monarchy) and the war with the Emirate of Trarza.
I personally believe, even if France is weaker than in the days of Napoleon, I think it's more than a match for Haiti.* Unless Haiti finds an ally in the new world to help, and I don't think the U.S. would be looking to help Haiti, not to mention the other states having only just gained independence, which only leaves the U.K...
...frankly, I think the Haitians are gonna lose and France would regain their wayward colony in such a scenario.
*which it might be, given that the largest army fielded by the Royalists during the Restoration era, was during the Trienio Liberal, which saw some 60,000 to restore absolutist rule in Spain, compared to during the Hundred Days, which saw the French Army totaling almost 5 times that amount...but I digress.